In comments to the newspaper 20 Minuten, the 24-year-old said the group had never intended to cause offence to a religion or culture.
“Following a five-day trek and wet weather we had the idea to take a photo of our naked buttocks,” the man, who wanted to remain anonymous, told the paper.
He said park wardens confronted them and told them to stop, which they did.
“The wardens were very friendly and said incidents like this happened regularly,” the tourist said. The group apologized and then left the site.
The Swiss said he thought they had got off with a warning, so was shocked when the story made world news after being picked up by AFP.
“It was a dumb idea,” he admitted.
The news agency reported at the end of last week that a 24-year-old Swiss tourist, a 21-year-old from Germany, and a 26-year-old from the Netherlands had been expelled from the site the previous Tuesday.
It quoted a local police official as saying the three had broken internal rules but had not been detained.
Peruvian authorities consider undressing at Machu Picchu disrespectful.
In June 2014 the Peruvian culture ministry had to issue a reminder that nudity is banned after a wave of visitors snapping offensive pictures.
The 15th century stone citadel built atop a mountain is the jewel in the crown of Peru's tourism industry and has been a Unesco world heritage site since 1983.